Students deepen their understanding of ratios to investigate proportional relationships, in order to solve multistep, realworld ratio problems using new strategies that rely on proportional reasoning.
In Unit 1, seventh grade students deepen their understanding of ratios to investigate and analyze proportional relationships. They begin the unit by looking at how proportional relationships are represented in tables, equations, and graphs. As they analyze each representation, students continue to internalize what proportionality means, and how concepts like the constant of proportionality are visible in different ways. Students then spend time comparing examples of proportional and nonproportional associations, and studying how all the representations are connected to one another. Finally, in this unit, students will solve multistep, realworld ratio and rate problems using efficient strategies and representations that rely on proportional reasoning (MP.4). These new strategies and representations, such as setting up and solving a proportion, are added to students’ growing list of approaches to solve problems. Throughout the unit, students will engage with MP.2 and MP.6. Translating between equations, graphs, tables, and written explanations requires students to reason both abstractly and quantitatively, and to pay precise attention to units, calculations, and forms of communication throughout their work.
In sixth grade, students were introduced to the concept of ratios and rates. They learned several strategies to represent ratios and to solve problems, including using concrete drawings, double number lines, tables, tape diagrams, and graphs. They defined and found unit rates and applied this to measurement conversion problems. Seventh grade students will draw on these conceptual understandings to fully understand proportional relationships.
Beyond this unit, in Unit 5, seventh grade students will reengage with proportional reasoning, solving percent problems and investigating how proportional reasoning applies to scale drawings. In eighth grade, students connect unit rate to slope, and they compare proportional relationships across different representations. They expand their understanding of nonproportional relationships to study linear functions in the form of $$y=mx+b$$, and compare these to nonlinear functions, such as $$y=6x^2$$.
Pacing: 22 instructional days (18 lessons, 3 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 20212022 school year, see our 7th Grade Scope and Sequence Recommended Adjustments.
This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the unit.
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Model  Example  
Setting up and solving a proportion 
A group of 4 students buy movie tickets for $24. At this rate, how much would 20 students pay for the movie? $$\frac{4\space \mathrm{students}}{$24} = \frac{20\space \mathrm{students}}{$x}$$ $$4x=24(20)$$ $$x=$120$$ 

Table of equivalent ratios 
The table below shows some weights of rice, in pounds, and their corresponding costs, in dollars.


Equation  The equation $$y=8.75x$$ represents the cost in dollars, $$y$$, to purchase $$x$$ pounds of turkey meat at a deli.  
Graph 
The graph below shows the relationship between the cost of gas and the number of gallons of gas purchased at a gas station. 
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constant of proportionality
equivalent ratio
ratio
unit rate
part to part ratio
part to whole ratio
commission
rate
dependent variable
proportion
independent variable
proportional relationship
To see all the vocabulary for this course, view our 7th Grade Vocabulary Glossary.
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To see more information about the materials in this unit, view the Unit Materials Overview.
Key: Major Cluster Supporting Cluster Additional Cluster
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